1. Field of the Invention
This invention relates to harmonic distortion analysis of waveforms in an A/C electrical system and, in particular, to an apparatus method by which a total harmonic distortion signal of reasonable accuracy can be repetitively generated without undue signal processing.
2. Background Information
There is increasing use of loads which can distort the sinusoidal waveforms, especially the current waveforms, in A/C power systems, and particularly, in power distribution systems. As such waveform distortion can adversely affect the equipment of other users on the system, and the revenues of the utility supplying the power, there is increased emphasis on locating the sources of and reducing the effects of such distortion.
It is well known to quantify the distortion in sinusoidal waveforms through harmonic analysis. Harmonic analysis is based on the principal that any periodic waveform can be characterized as the sum of a sine wave at the fundamental frequency and sine waves at harmonics of the fundamental frequency. One standard measure of harmonic distortion is individual harmonic distortion. This is a measure of the distortion attributable to a specific harmonic. Individual harmonic distortion is measured as the RMS value of the particular harmonic as a percentage of the RMS value of the fundamental frequency. Another standard measure of harmonic distortion is the total harmonic distortion. Typically, total harmonic distortion is calculated as the ratio of the square root of the sum of the squares of the RMS values of the individual harmonics not including the fundamental to the RMS value of the fundamental converted to a percentage.
Thus, the typical total harmonic calculation requires calculation of the individual harmonics. As is well known, the values of the harmonics and the fundamental frequency component can be extracted from digital samples of the A/C waveform by use of Fourier analysis. This analysis produces sine and cosine coefficients for the fundamental and each of the harmonics to be analyzed. In many applications there is interest in the magnitudes of a large number of harmonics, for instance, up to the fiftieth harmonic. Compounding the problem is the fact that a waveform must be digitally sampled at twice the frequency of the highest harmonic to be extracted. Therefore, in order to extract the fiftieth harmonic from a waveform with 60 Hz fundamental frequency, sampling must be performed at 6 KHz. It can be appreciated then that analyzers must have processors which can sample at the high sampling rate needed to extract the desired harmonics, and can also perform the extensive calculations required for the Fourier analysis. Typically, analyzers sample for one or a few cycles and then suspend sampling while the harmonic coefficients are calculated. This technique degrades the ability of the analyzer to catch transients in the waveforms. Some analyzers trigger the high speed sampling required for harmonic analysis upon detection of specific events, thereby capturing the portion of the waveform of interest.
In an effort to reduce the burden on the analyzer processor, an approximation has been used for determining total harmonic distortion. This approximation calculates the square root of the difference between the square of the RMS value of the total signal minus the square of the RMS value of the fundamental divided by the RMS value of the fundamental and converted to a percentage. Thus, this approximation only requires the calculation of the harmonic coefficients for the fundamental frequency. However, when this approximation is used, the result is obtained by taking the square root of the difference between two numbers. If the total harmonic distortion is a small percent, high precision of the two numbers generating the difference is required. As an example, a one percent THD where the fundamental frequency is 100 Hz is the square root of (10001-10000). This implies that an accuracy of about 0.01 percent in the measurement and calculation of the waveform values is required to obtain a one percent THD accuracy.
There is a need for an improved apparatus for determining harmonic distortion in A/C waveforms.
More particularly, there is a need for an improved apparatus for determining total harmonic distortion in an A/C waveform which reduces the burden on a digital processor generating the total harmonic distortion signal from digital samples of the waveform.
There is also a need for such an improved apparatus which generates an approximation of total harmonic distortion in an ac waveform rapidly yet with a reasonable accuracy.